Justice KAGANdelivered the opinion of the Court.
For the second time in little more than a decade, Kansas and Nebraska ask this Court to settle a dispute over the States'
*1049rights to the waters of the Republican River Basin, as set out in an interstate compact. The first round of litigation ended with a settlement agreement designed to elaborate on, and promote future compliance with, the Compact's terms. The States now bring new claims against each other arising from the implementation of that settlement. Kansas seeks exceptional relief-both partial disgorgement of gains and an injunction-for Nebraska's conceded overconsumption of water. For its part, Nebraska requests amendment of a technical appendix to the settlement, so that allocations of water will faithfully reflect the parties' intent as expressed in both the body of that agreement and the Compact itself. We referred the case to a Special Master and now accept his recommendations as to appropriate equitable remedies: for Kansas, partial disgorgement but no injunction; and for Nebraska, reform of the appendix.
I
The Republican River originates in Colorado; crosses the northwestern corner of Kansas into Nebraska; flows through much of southwestern Nebraska; and finally cuts back into northern Kansas. Along with its many tributaries, the river drains a 24,900-square-mile watershed, called the Republican River Basin. The Basin contains substantial farmland, producing (among other things) wheat and corn.
During the Dust Bowl of the 1930's, the Republican River Basin experienced an extended drought, interrupted once by a deadly flood. In response, the Federal Government proposed constructing reservoirs in the Basin to control flooding, as well as undertaking an array of irrigation projects to disperse the stored water. But the Government insisted that the three States of the Basin first agree to an allocation of its water resources. As a result of that prodding, the States negotiated and ratified the Republican River Compact; and in 1943, as required under the Constitution, Art. I, § 10, cl. 3, Congress approved that agreement. By act of Congress, the Compact thus became federal law. See Act of May 26, 1943, ch. 104, 57 Stat. 86.
The Compact apportions among the three States the "virgin water supply originating in"-and, as we will later discuss, originating onlyin-the Republican River Basin. Compact Art. III; see infra,at 1059 - 1064. "Virgin water supply," as used in the Compact, means "the water supply within the Basin," in both the River and its tributaries, "undepleted by the activities of man." Compact Art. II. The Compact gives each State a set share of that supply-roughly, 49% to Nebraska, 40% to Kansas, and 11% to Colorado-for any "beneficial consumptive use." Id.,Art. IV; see Art. II (defining that term to mean "that use by which the water supply of the Basin is consumed through the activities of man"). In addition, the Compact charges the chief water official of each State with responsibility to jointly administer the agreement. See id.,Art. IX. Pursuant to that provision, the States created the Republican River Compact Administration (RRCA). The RRCA's chief task is to calculate the Basin's annual virgin water supply by measuring stream flow throughout the area, and to determine (retrospectively) whether each State's use of that water has stayed within its allocation.
All was smooth sailing for decades, until Kansas complained to this Court about Nebraska's increased pumping of groundwater, resulting from that State's construction of "thousands of wells hydraulically connected to the Republican River and its tributaries." Bill of Complaint, *1050O.T. 1997, No. 126, Orig., p. 5 (May 26, 1998). Kansas contended that such activity was subject to the Compact: To the extent groundwater pumping depleted stream flow in the Basin, it counted against the pumping State's annual allotment of water.1Nebraska maintained, to the contrary, that groundwater pumping fell outside the Compact's scope, even if that activity diminished stream flow in the area. A Special Master we appointed favored Kansas's interpretation of the Compact; we summarily agreed, and recommitted the case to him for further proceedings. See Kansas v. Nebraska,530 U.S. 1272, 120 S.Ct. 2764, 147 L.Ed.2d 1003 (2000). The States then entered into negotiations, aimed primarily at determining how best to measure, and reflect in Compact accounting, the depletion of the Basin's stream flow due to groundwater pumping. During those discussions, the States also addressed a range of other matters affecting Compact administration. The talks bore fruit in 2002, when the States signed the Final Settlement Stipulation (Settlement).
The Settlement established detailed mechanisms to promote compliance with the Compact's terms. The States agreed that the Settlement was not "intended to, nor could [it], change [their] respective rights and obligations under the Compact." Settlement § I(D). Rather, the agreement aimed to accurately measure the supply and use of the Basin's water, and to assist the States in staying within their prescribed limits. To smooth out year-to-year fluctuations and otherwise facilitate compliance, the Settlement based all Compact accounting on 5-year running averages, reduced to 2-year averages in "water-short" periods. Id.,§§ IV(D), V(B). That change gave each State a chance to compensate for one (or more) year's overuse with another (or more) year's underuse before exceeding its allocation. The Settlement further provided, in line with this Court's decision, that groundwater pumping would count as part of a State's consumption to the extent it depleted the Basin's stream flow. An appendix to the agreement called the "Accounting Procedures" described how a later-developed "Groundwater Model" (essentially, a mass of computer code) would perform those computations. Id.,App. C; id.,App. J1. And finally, the Settlement made clear, in accordance with the Compact, that a State's use of "imported water"-that is, water farmers bring into the area (usually for irrigation) that eventually seeps into the Republican River-would not count toward the State's allocation, because it did not originate in the Basin. Id., §§ II, IV(F). Once again, the Settlement identified the Accounting Procedures and Groundwater Model as the tools to calculate (so as to exclude) that consumption.
But there were more rapids ahead: By 2007, Kansas and Nebraska each had complaints about how the Settlement was working. Kansas protested that in the 2005-2006 accounting period-the first for which the Settlement held States responsible-Nebraska had substantially exceeded its allocation of water. Nebraska, for its part, maintained that the Accounting Procedures and Groundwater Model were charging the State for use of imported water-specifically, for water originating in the Platte River Basin. The States brought those disputes to the RRCA and then to non-binding arbitration, in accordance with the Settlement's dispute resolution *1051provisions. After failing to resolve the disagreements in those forums, Kansas sought redress in this Court, petitioning for both monetary and injunctive relief. We referred the case to a Special Master to consider Kansas's claims. See 563 U.S. ----, 131 S.Ct. 378, 178 L.Ed.2d 14 (2011). In that proceeding, Nebraska asserted a counterclaim requesting a modification of the Accounting Procedures to ensure that its use of Platte River water would not count toward its Compact allocation.
After two years of conducting hearings, receiving evidence, and entertaining legal arguments, the Special Master issued his report and recommendations. The Master concluded that Nebraska had "knowingly failed" to comply with the Compact in the 2005-2006 accounting period, by consuming 70,869 acre-feet of water in excess of its prescribed share.2Report 112. To remedy that breach, the Master proposed awarding Kansas $3.7 million for its loss, and another $1.8 million in partial disgorgement of Nebraska's still greater gains. The Master, however, thought that an injunction against Nebraska was not warranted. In addition, the Master recommended reforming the Accounting Procedures in line with Nebraska's request, to ensure that the State would not be charged with using Platte River water.
Kansas and Nebraska each filed exceptions in this Court to parts of the Special Master's report.3Nebraska objects to the Master's finding of a "knowing" breach and his call for partial disgorgement of its gains. Kansas asserts that the Master should have recommended both a larger disgorgement award and injunctive relief; the State also objects to his proposed change to the Accounting Procedures. In reviewing those claims, this Court gives the Special Master's factual findings "respect and a tacit presumption of correctness." Colorado v. New Mexico,467 U.S. 310, 317, 104 S.Ct. 2433, 81 L.Ed.2d 247 (1984). But we conduct an "independent review of the record," and assume "the ultimate responsibility for deciding" all matters. Ibid.Having carried out that careful review, we now overrule all exceptions and adopt the Master's recommendations.
II
The Constitution gives this Court original jurisdiction to hear suits between the States. See Art. III, § 2. Proceedings under that grant of jurisdiction are "basically equitable in nature." Ohio v. Kentucky,410 U.S. 641, 648, 93 S.Ct. 1178, 35 L.Ed.2d 560 (1973). When the Court exercises its original jurisdiction over a controversy between two States, it serves "as a substitute for the diplomatic settlement of controversies between sovereigns and a possible resort to force." North Dakota v. Minnesota,263 U.S. 365, 372-373, 44 S.Ct. 138, 68 L.Ed. 342 (1923). That role significantly "differ[s] from" the one the Court undertakes "in suits between private parties." Id.,at 372, 44 S.Ct. 138; see Frankfurter & Landis, The Compact Clause of the Constitution-A Study in Interstate Adjustments, 34 Yale L.J. 685, 705 (1925)(When a "controversy concerns two States we are at once in a world wholly different from that of a law-suit between John Doe *1052and Richard Roe over the metes and bounds of Blackacre"). In this singular sphere, "the court may regulate and mould the process it uses in such a manner as in its judgment will best promote the purposes of justice." Kentucky v. Dennison,24 How. 66, 98, 16 L.Ed. 717 (1861).
Two particular features of this interstate controversy further distinguish it from a run-of-the-mill private suit and highlight the essentially equitable character of our charge. The first relates to the subject matter of the Compact and Settlement: rights to an interstate waterway. The second concerns the Compact's status as not just an agreement, but a federal law. Before proceeding to the merits of this dispute, we say a few words about each.
This Court has recognized for more than a century its inherent authority, as part of the Constitution's grant of original jurisdiction, to equitably apportion interstate streams between States. In Kansas v. Colorado,185 U.S. 125, 145, 22 S.Ct. 552, 46 L.Ed. 838 (1902), we confronted a simple consequence of geography: An upstream State can appropriate all water from a river, thus "wholly depriv[ing]" a downstream State "of the benefit of water" that "by nature" would flow into its territory. In such a circumstance, the downstream State lacks the sovereign's usual power to respond-the capacity to "make war[,] ... grant letters of marque and reprisal," or even enter into agreements without the consent of Congress. Id.,at 143, 22 S.Ct. 552(internal quotation marks omitted). "Bound hand and foot by the prohibitions of the Constitution, ... a resort to the judicial power is the only means left" for stopping an inequitable taking of water. Id.,at 144, 22 S.Ct. 552(quoting Rhode Island v. Massachusetts,12 Pet. 657, 726, 9 L.Ed. 1233 (1838)).
This Court's authority to apportion interstate streams encourages States to enter into compacts with each other. When the division of water is not "left to the pleasure" of the upstream State, but States instead "know[ ] that some tribunal can decide on the right," then "controversies will [probably] be settled by compact." Kansas v. Colorado,185 U.S., at 144, 22 S.Ct. 552. And that, of course, is what happened here: Kansas and Nebraska negotiated a compact to divide the waters of the Republican River and its tributaries. Our role thus shifts: It is now to declare rights under the Compact and enforce its terms. See Texas v. New Mexico,462 U.S. 554, 567, 103 S.Ct. 2558, 77 L.Ed.2d 1 (1983).
But in doing so, we remain aware that the States bargained for those rights in the shadow of our equitable apportionment power-that is, our capacity to prevent one State from taking advantage of another. Each State's "right to invoke the original jurisdiction of this Court [is] an important part of the context" in which any compact is made. Id.,at 569, 103 S.Ct. 2558. And it is "difficult to conceive" that a downstream State "would trade away its right" to our equitable apportionment if, under such an agreement, an upstream State could avoid its obligations or otherwise continue overreaching. Ibid.Accordingly, our enforcement authority includes the ability to provide the remedies necessary to prevent abuse. We may invoke equitable principles, so long as consistent with the compact itself, to devise "fair ... solution[s]" to the state-parties' disputes and provide effective relief for their violations. Texas v. New Mexico,482 U.S. 124, 134, 107 S.Ct. 2279, 96 L.Ed.2d 105 (1987)(supplying an "additional enforcement mechanism" to ensure an upstream State's compliance with a compact).4
*1053And that remedial authority gains still greater force because the Compact, having received Congress's blessing, counts as federal law. See Cuyler v. Adams,449 U.S. 433, 438, 101 S.Ct. 703, 66 L.Ed.2d 641 (1981)("[C]ongressional consent transforms an interstate compact ... into a law of the United States"). Of course, that legal status underscores a limit on our enforcement power: We may not "order relief inconsistent with [a compact's] express terms." Texas v. New Mexico,462 U.S., at 564, 103 S.Ct. 2558. But within those limits, the Court may exercise its full authority to remedy violations of and promote compliance with the agreement, so as to give complete effect to public law. As we have previously put the point: When federal law is at issue and "the public interest is involved," a federal court's "equitable powers assume an even broader and more flexible character than when only a private controversy is at stake." Porter v. Warner Holding Co.,328 U.S. 395, 398, 66 S.Ct. 1086, 90 L.Ed. 1332 (1946); see Virginian R. Co. v. Railway Employees,300 U.S. 515, 552, 57 S.Ct. 592, 81 L.Ed. 789 (1937)("Courts of equity may, and frequently do, go much farther" to give "relief in furtherance of the public interest than they are accustomed to go when only private interests are involved").5In exercising our jurisdiction, we may "mould each decree to the necessities of the particular case" and "accord full justice" to all parties.Porter,328 U.S., at 398, 66 S.Ct. 1086(internal quotation marks omitted); see Kentucky v. Dennison,65 U.S., at 98. These principles inform our consideration of the dispute before us.
III
We first address Nebraska's breach of the Compact and Settlement and the remedies appropriate to that violation. Both parties assent to the Special Master's finding that in 2005-2006 Nebraska exceeded its allocation of water by 70,869 acre-feet-about 17% more than its proper share. See Report 88-89; App. B to Reply Brief for Kansas. They similarly agree that this overconsumption resulted in a $3.7 million loss to Kansas; and Nebraska has agreed to pay those damages. See Reply Brief for Kansas 9, 55; Brief for Nebraska 7. But the parties dispute whether Nebraska's conduct warrants additional relief. The Master determined that Nebraska "knowingly exposed Kansas to a substantial risk" of breach, and so "knowingly failed" to comply with the Compact. Report 130, 112; see supra,at 1050 - 1051. Based in part on that finding, he recommended disgorgement of $1.8 million, which he described as "a small portion of *1054the amount by which Nebraska's gain exceeds Kansas's loss." Report 179. But he declined to grant Kansas's request for injunctive relief against Nebraska. See id.,at 180-186. As noted previously, see supra,at 1050 - 1051, each party finds something to dislike in the Master's handling of this issue: Nebraska contests his finding of a "knowing" Compact violation and his view that disgorgement is appropriate; Kansas wants a larger disgorgement award and an injunction regulating Nebraska's future conduct. We address those exceptions in turn.
A
When they entered into the Settlement in 2002, the States understood that Nebraska would have to significantly reduce its consumption of Republican River water. See Report 106. The Settlement, after all, charged Nebraska for its depletion of the Basin's stream flow due to groundwater pumping-an amount the State had not previously counted toward its allotment. See supra,at 1049 - 1050. Nebraska did not have to achieve all that reduction in the next year: The Settlement's adoption of multi-year averages to measure consumption allowed the State some time-how much depended on whether and when "water-short" conditions existed-to come into compliance. See Settlement §§ IV(D), V(B)(2)(e)(i), App. B; supra,at 1050. As it turned out, the area experienced a drought in 2006; accordingly, Nebraska first needed to demonstrate compliance in that year, based on the State's average consumption of water in 2005 and 2006.6And at that initial compliance check, despite having enjoyed several years to prepare, Nebraska came up markedly short.
Nebraska contends, contrary to the Master's finding, that it could not have anticipated breaching the Compact in those years. By its account, the State took "persistent and earnest"-indeed, "extraordinary"-steps to comply with the agreement, including amending its water law to reduce groundwater pumping. Brief for Nebraska 9, 17. And Nebraska could not have foreseen (or so it claims) that those measures would prove inadequate. First, Nebraska avers, drought conditions between 2002 and 2006 reduced the State's yearly allotments to historically low levels; the Master was thus "unfair to suggest Nebraska should have anticipated what never before was known." Id.,at 17. And second, Nebraska stresses, the RRCA determines each State's use of water only retrospectively, calculating each spring what a State consumed the year before; hence, Nebraska "could not have known" that it was out of compliance in 2006 "until early 2007-when it was already too late." Id.,at 18; see supra,at 1049 - 1050.
But that argument does not hold water: Rather, as the Special Master found, Nebraska failed to put in place adequate mechanisms for staying within its allotment in the face of a known substantial risk that it would otherwise violate Kansas's rights. See Report 105-112, 130. As an initial matter, the State's efforts to reduce its use of Republican River water came at a snail-like pace. The Nebraska Legislature waited a year and a half after signing the Settlement to amend the State's water law. See § 55, 2004 Neb. Laws p. 352, codified at Neb.Rev.Stat. 46-715. And the fix the legislature adopted-the development of regional water management *1055plans meant to decrease groundwater pumping-did not go into effect for still another year. Nebraska thus wasted the time following the Settlement-a crucial period to begin bringing down the State's consumption. Indeed, the State's overuse of Republican River water actually rose significantly from 2003 through 2005, making compliance at the eventual day of reckoning ever more difficult to achieve. See Report 108-109.7And to make matters worse, Nebraska knew that decreasing pumping does not instantly boost stream flow: A time lag, of as much as a year, exists between the one and the other. See id.,at 106. So Nebraska's several-year delay in taking any corrective action foreseeably raised the risk that the State would breach the Compact.
Still more important, what was too late was also too little. The water management plans finally adopted in 2005 called for only a 5% reduction in groundwater pumping, although no evidence suggested that would suffice. The testimony presented to the Special Master gave not a hint that the state and local officials charged with formulating those plans had conducted a serious appraisal of how much change would be necessary. See id.,at 107-108. And the State had created no way to enforce even the paltry goal the plans set. The Nebraska Legislature chose to leave operational control of water use in the hands of district boards consisting primarily of irrigators, who are among the immediate beneficiaries of pumping. No sanctions or other mechanisms held those local bodies to account if they failed to meet the plans' benchmark. They bore no legal responsibility for complying with the Compact, and assumed no share of the penalties the State would pay for violations. See id.,at 110-111. Given such a dearth of tools or incentives to achieve compliance, the wonder is only that Nebraska did not still further exceed its allotment.
Nor do Nebraska's excuses change our view of its misbehavior. True enough, the years following the Settlement were exceptionally arid. But the Compact and Settlement (unsurprisingly) contemplate wet and dry years alike. By contrast, Nebraska's plans could have brought it into compliance only if the Basin had received a stretch of copious rainfall. See id.,at 109-110. And Nebraska cannot take refuge in the timing of the RRCA's calculations. By the time the compliance check of 2006 loomed, Nebraska knew that it had exceeded its allotment (by an ever greater margin) in each of the three previous years. As Nebraska's own witnesses informed the Special Master, they "could clearly see" by the beginning of 2006 "that [the State] had not done enough" to come into compliance. Id.,at 109 (quoting Tr. 1333 (Aug. 21, 2012)). Indeed, in that year, Nebraska began purchasing its farmers' rights to surface water in order to mitigate its anticipated breach. But that last-minute effort, in the Master's words, "fell woefully short"-as at that point could only have been expected. Report 109. From the outset of the Settlement through 2006, Nebraska headed-absent the luckiest of circumstances-straight toward a Compact violation.
For these reasons, we agree with the Master's conclusion that Nebraska "knowingly exposed Kansas to a substantial risk" of receiving less water than the Compact provided, and so "knowingly failed" to comply with the obligations that agreement imposed. Id.,at 130, 112. In the *1056early years of the Settlement, as the Master explained, Nebraska's compliance efforts were not only inadequate, but also "reluctant," showing a disinclination "to take [the] firm action" necessary "to meet the challenges of foreseeably varying conditions in the Basin." Id.,at 105. Or said another way, Nebraska recklessly gambled with Kansas's rights, consciously disregarding a substantial probability that its actions would deprive Kansas of the water to which it was entitled. See Tr. 1870 (Aug. 23, 2012) (Master's statement that Nebraska showed "reckless indifference as to compliance back in '05 and '06").
After determining that Kansas lost $3.7 million from Nebraska's breach, the Special Master considered the case for an additional monetary award. Based on detailed evidence, not contested here, he concluded that an acre-foot of water is substantially more valuable on farmland in Nebraska than in Kansas. That meant Nebraska's reward for breaching the Compact was "much larger than Kansas' loss, likely by more than several multiples." Report 178. Given the circumstances, the Master thought that Nebraska should have to disgorge part of that additional gain, to the tune of $1.8 million. In making that recommendation, he relied on his finding-which we have just affirmed-of Nebraska's culpability. See id.,at 130. He also highlighted this Court's broad remedial powers in compact litigation, noting that such cases involve not private parties' private quarrels, but States' clashes over federal law. See id.,at 131, 135; supra,at 1051 - 1053.
Nebraska (along with the dissent) opposes the Special Master's disgorgement proposal on the ground that the State did not "deliberately act[ ]" to violate the Compact. Reply Brief for Nebraska 33; see post,at 1051 - 1052. Relying on private contract law, Nebraska cites a Restatement provision declaring that a court may award disgorgement in certain cases in which "a deliberate breach of contract results in profit to the defaulting promisor." Restatement (Third) of Restitution and Unjust Enrichment § 39(1) (2010)(Restatement); see Reply Brief for Nebraska 32. Nebraska then points out that the Master, even though finding a "knowing" exposure of Kansas to significant risk, rejected the idea that "Nebraska officials [had] deliberately set out to violate the Compact." Brief for Nebraska 16 (quoting Report 111). Accordingly, Nebraska concludes, no disgorgement is warranted.
But that argument fails to come to terms with what the Master properly understood as the wrongful nature of Nebraska's conduct. True enough, as the Master said, that Nebraska did not purposefully set out to breach the Compact. But still, as he also found, the State "knowingly exposed Kansas to a substantial risk" of breach, and blithely proceeded. Report 130. In some areas of the law and for certain purposes, the distinction between purposefully invading and recklessly disregarding another's rights makes no difference. See Bullock v. BankChampaign, N.A.,569 U.S. ----, ----, 133 S.Ct. 1754, 1759, 185 L.Ed.2d 922 (2013)("We include as intentional ... reckless conduct" of the kind that the law "often treats as the equivalent"); Ernst & Ernst v. Hochfelder,425 U.S. 185, 193-194, n. 12, 96 S.Ct. 1375, 47 L.Ed.2d 668 (1976)("[R]ecklessness is [sometimes] considered to be a form of intentional conduct for purposes of imposing liability"). And indeed, the very Restatement Nebraska relies on treats the two similarly. It assimilates "deliberate[ness]" to "conscious wrongdoing," which it defines as acting (as Nebraska did) "despite a known risk that the conduct ... violates [another's] rights." Restatement *1057§ 39, Comment f; id.,§ 51(3). Conversely, the Restatement distinguishes "deliberate[ness]" from behavior (not akin to Nebraska's) amounting to mere "inadvertence, negligence, or unsuccessful attempt at performance." Id.,§ 39, Comment f.
And whatever is true of a private contract action, the case for disgorgement becomes still stronger when one State gambles with another State's rights to a scarce natural resource. From the time this Court began to apportion interstate rivers, it has recognized part of its role as guarding against upstream States' inequitable takings of water. And as we have noted, that concern persists even after States enter into a compact: This Court may then exercise remedial authority to ensure compliance with the compact's terms-thus preventing a geographically favored State from appropriating more than its share of a river. See supra,at 1052. Indeed, the formation of such a compact provides this Court with enhanced remedial power because, as we have described, the agreement is also an Act of Congress, and its breach a violation of federal law. See supra,at 1052 - 1053; Porter,328 U.S. 395, 66 S.Ct. 1086(exercising equitable power to disgorge profits gained from violating a federal statute). Consistent with those principles, we have stated that awarding actual damages for a compact's infringement may be inadequate, because that remedy alone "would permit [an upstream State] to ignore its obligation to deliver water as long as it is willing" to pay that amount. Texas v. New Mexico,482 U.S., at 132, 107 S.Ct. 2279. And as the Solicitor General noted in argument here, "[i]t is important that water flows down the river, not just money." Tr. of Oral Arg. 24. Accordingly, this Court may order disgorgement of gains, if needed to stabilize a compact and deter future breaches, when a State has demonstrated reckless disregard of another, more vulnerable State's rights under that instrument.
Assessed in this light, a disgorgement order constitutes a "fair and equitable" remedy for Nebraska's breach. Texas v. New Mexico, 482 U.S., at 134, 107 S.Ct. 2279. "Possessing the privilege of being upstream," Nebraska can (physically, though not legally) drain all the water it wants from the Republican River. Report 130. And the higher value of water on Nebraska's farmland than on Kansas's means that Nebraska can take water that under the Compact should go to Kansas, pay Kansas actual damages, and still come out ahead. That is nearly a recipe for breach-for an upstream State to refuse to deliver to its downstream neighbor the water to which the latter is entitled. And through 2006, Nebraska took full advantage of its favorable position, eschewing steps that would effectively control groundwater pumping and thus exceeding its allotment. In such circumstances, a disgorgement award appropriately reminds Nebraska of its legal obligations, deters future violations, and promotes the Compact's successful administration. See Porter,328 U.S., at 400, 66 S.Ct. 1086("Future compliance may be more definitely assured if one is compelled to restore one's illegal gains").8We thus reject Nebraska's *1058exception to the Master's proposed remedy.
B
Kansas assails the Special Master's recommended disgorgement award from the other direction, claiming that it is too low to ensure Nebraska's future compliance. See Brief for Kansas 55-59. Notably, Kansas does not insist on all of Nebraska's gain. It recognizes the difficulty of ascertaining that figure, given the evidence the parties presented. See id.,at 56; see also Report 177-178. And still more important, it "agrees" with the Master's view that the Court should select a "fair point on th[e] spectrum" between no profits and full profits, based on the totality of facts and interests in the case. Brief for Kansas 57 (quoting Report 135); see Sur-Reply Brief for Kansas 5. In setting that point, however, Kansas comes up with a higher number-or actually, a trio of them. The State first asks us to award "treble damages of $11.1 million," then suggests that we can go "up to roughly $25 million," and finally proposes a "1:1 loss-to-disgorgement ratio," which means $3.7 million of Nebraska's gains. Brief for Kansas 57; Sur-Reply Brief for Kansas 5, 7.
We prefer to stick with the Master's single number. As an initial matter, we agree with both the Master and Kansas that disgorgement need not be all or nothing. See, e.g.,1 D. Dobbs, Law of Remedies § 2.4(1), p. 92 (2d ed. 1993) ("Balancing of equities and hardships may lead the court to grant some equitable relief but not" the full measure requested); Restatement § 39, Comment i; id.,§ 50, Comment a; National Security Systems, Inc. v. Iola,700 F.3d 65, 80-81, 101-102 (C.A.3 2012). In exercising our original jurisdiction, this Court recognizes that "flexibility [is] inherent in equitable remedies," Brown v. Plata,563 U.S. ----, ----, 131 S.Ct. 1910, 1944, 179 L.Ed.2d 969 (2011)(quoting Hutto v. Finney,437 U.S. 678, 687, n. 9, 98 S.Ct. 2565, 57 L.Ed.2d 522 (1978)), and awards them "with reference to the facts of the particular case," Texas v. New Mexico,482 U.S., at 131, 107 S.Ct. 2279(quoting Haffner v. Dobrinski,215 U.S. 446, 450, 30 S.Ct. 172, 54 L.Ed. 277 (1910)). So if partial disgorgement will serve to stabilize a compact by conveying an effective message to the breaching party that it must work hard to meet its future obligations, then the Court has discretion to order only that much. Cf. Kansas v. Colorado,533 U.S. 1, 14, 121 S.Ct. 2023, 150 L.Ed.2d 72 (2001)(concluding that a master "acted properly in carefully analyzing the facts of the case and in only awarding as much prejudgment interest as was required by a balancing of the equities").
And we agree with the Master's judgment that a relatively small disgorgement award suffices here. That is because, as the Master detailed, Nebraska altered its conduct after the 2006 breach, and has complied with the Compact ever since. See Report 112-118, 180. In 2007, Nebraska enacted new legislation establishing a mechanism to accurately forecast the State's annual allotment of Republican River water. § 23, 2007 Neb. Laws p. 1600, codified at Neb.Rev.Stat. 46-715(6). Further, a new round of water management plans called for localities to reduce groundwater pumping by five times as much as the old (5%) target. And most important, those plans implemented a system for the State, in dry years, to force districts to curtail both surface water use and groundwater pumping. That "regulatory back-stop," as Nebraska calls it, corrects the State's original error of leaving all control *1059of water use to unaccountable local actors. Report 113 (quoting Direct Testimony of Brian Dunnigan, Director, Nebraska Department of Resources ¶ 43 (July 25, 2012)); see supra,at 1054 - 1055. Testimony before the Master showed that if the scheme had been in effect between 2002 and 2006, Nebraska would have lived within its allocation throughout that period. See Report 117. The Master thus reasonably concluded that the current water management plans, if implemented in good faith, "will be effective to maintain compliance even in extraordinarily dry years." See id.,at 118. And so the Master had good cause to recommend the modest award he did, which serves as an ever-present reminder to Nebraska, but does not assume its continuing misconduct.
Truth be told, we cannot be sure why the Master selected the exact number he did-why, that is, he arrived at $1.8 million, rather than a little more or a little less. The Master's Report, in this single respect, contains less explanation than we might like. But then again, any hard number reflecting a balance of equities can seem random in a certain light-as Kansas's own briefs, with their ever-fluctuating ideas for a disgorgement award, amply attest. What matters is that the Master took into account the appropriate considerations-weighing Nebraska's incentives, past behavior, and more recent compliance efforts-in determining the kind of signal necessary to prevent another breach. We are thus confident that in approving the Master's recommendation for about half again Kansas's actual damages, we award a fair and equitable remedy suited to the circumstances.
For related reasons, we also reject Kansas's request for an injunction ordering Nebraska to comply with the Compact and Settlement. Kansas wants such an order so that it can seek contempt sanctions against Nebraska for any future breach. See Brief for Kansas 36-44. But we agree with the Master that Kansas has failed to show, as it must to obtain an injunction, a "cognizable danger of recurrent violation." United States v. W.T. Grant Co.,345 U.S. 629, 633, 73 S.Ct. 894, 97 L.Ed. 1303 (1953). As just discussed, Nebraska's new compliance measures, so long as followed, are up to the task of keeping the State within its allotment. And Nebraska is now on notice that if it relapses, it may again be subject to disgorgement of gains-either in part or in full, as the equities warrant. That, we trust, will adequately guard against Nebraska's repeating its former practices.
IV
The final question before us concerns the Special Master's handling of Nebraska's counterclaim. As we have noted, Nebraska contended that the Settlement's Accounting Procedures inadvertently charge the State for using "imported water"-specifically, water from the Platte River-in conflict with the parties' intent in both the Compact and the Settlement. See supra,at 1050 - 1051. The Master agreed, and recommended modifying the Procedures by adopting an approach that the parties call the "5-run formula," to ensure that Nebraska's consumption of Platte River water will not count toward its Compact allotment. Kansas now objects to that proposed remedy.
The Compact, recall, apportions the virgin water supply of the Republican River and its tributaries-nothing less, but also nothing more. See Compact Art. III; supra,at 1049. One complexity of that project arises from water's ... well, fluid quality. Nebraska imports water from the Platte River, outside the Republican River Basin and thus outside the Compact's scope, to irrigate farmland. And that imported *1060water simply will not stay still: Some of it seeps through the ground and raises stream flow in the Republican River and its tributaries. See Second Report of Special Master, O.T. 1999, No. 126, Orig., pp. 62-63 (Second Report). In negotiating the Settlement, the States undertook-as part of their effort to accurately apportion the Basin'swater-to exclude all such imported water from their calculations. Reflecting the Compact's own scope, § IV(F) of the Settlement states, in no uncertain terms, that "Beneficial Consumptive Use of Imported Water Supply shall not count as Computed Beneficial Consumptive Use" of Republican River Basin water. Which means, without all that distracting capitalization, that when Nebraska consumes imported water that has found its way into the Basin's streams, that use shall not count toward its Compact allotment. But that edict of course requires calculating (in order to exclude) the State's consumption of imported water. The Settlement's Accounting Procedures, in tandem with its Groundwater Model, are the tools the parties employ to make that computation.
But as the Master found, the Procedures (and Model) founder in performing that task in dry conditions: They treat Nebraska's use of imported water as if it were use of Basin water. That failure flows from the way the Procedures measure a State's consumption of water resulting from groundwater pumping. According to the Settlement, such pumping is to count against a State's allotment only to the extent it reduces stream flow in specified areas-which it rarely does in a 1-to-1 ratio and sometimes does not do at all. See id.,§ IV(C)(1); Report 19; n. 1, supra.Most notable here, pumping cannot deplete an already wholly dry stream-and in arid conditions, some of the Basin's tributaries in fact run dry. As the Master put the point, stream flow in a given area "fall[s] as groundwater pumping increases until it hits zero, at which point it falls no more even as groundwater pumping continues." Report 34. When that point arrives, Nebraska's continued pumping should not count as consumption of the Basin's virgin water. But-and here lies the rub-imported water (from the Platte) can create stream flow in what would otherwise be a dry riverbed. And the Accounting Procedures (and Model) fail to account for that possibility; accordingly, they see depletion of the Basin's stream flow-the sole measure of the State's consumption-where they should not. The result is to count imported water toward the State's consumption of Basin water. In 2006, for example, the Procedures charged Nebraska with using 7,797 acre-feet of Platte River water, over 4% of the State's allotment. By our estimate, just that single year's miscalculation cost Nebraska over $1 million. See id.,at 37, 176.
The Master specifically determined, and our review of the relevant testimony confirms, that the parties did not know the Accounting Procedures would have that effect. See id.,at 23-32. The States intended the Procedures (as per the Compact and Settlement) to count only consumption of the Basin's own water supply-and correlatively, to exclude use of water from the Platte. See id.,at 23-25; see also Second Report 37, 64 (same conclusion reached by the Special Master approving the Settlement). There is no evidence that anyone seriously thought, much less discussed, that the Accounting Procedures might systematically err in accomplishing those computations. See Report 26-27.9And because *1061no one knew of the fault in the Procedures, no one could possibly trade it off for other items during the parties' negotiations. Thus, as the Master found, Nebraska did not receive anything, nor did Kansas give up anything, in exchange for the (unknown) error. See id.,at 28-31. To the contrary, as all witnesses explained, the designers of the Procedures worked single-mindedly to implement the Compact's and Settlement's strict demarcation between virgin and imported water-and assumed they had succeeded. See id.,at 31-32.
But even if all that is so, Kansas argues (along with the dissent) that a deal is a deal is a deal-and this deal did not include the 5-run formula the Master now proposes. See Brief for Kansas 31-34; post, at 1072 - 1074. On that view, the parties' clear intent to exclude imported water does not matter; nor does their failure to appreciate that the Procedures, in opposition to that goal, would count such water in material amounts. According to Kansas, so long as the parties bargained (as they did) for the Procedures they got, that is the end of the matter: No one should now be heard to say that there is a better mode of accounting. See Tr. of Oral Arg. 54-55.
That argument, however, does not pass muster. Of course, courts generally hold parties to the deals they make; and of course, courts should hesitate, and then hesitate some more, before modifying a contract, even to remove an inadvertent flaw. But in this Compact case, two special (and linked) considerations warrant reforming the Accounting Procedures as the Master has proposed-or better phrased, warrant conforming those Procedures to the parties' underlying agreements. First, that remedy is necessary to prevent serious inaccuracies from distorting the States' intended apportionment of interstate waters, as reflected in both the Compact and the Settlement. And second, it is required to avert an outright breach of the Compact-and so a violation of federal law. We address each point in turn.
In resolving water disputes, this Court has opted to correct subsidiary technical agreements to promote accuracy in apportioning waters under a compact. In Texas v. New Mexico,for example, the parties entered into a compact that based division of the Pecos River on certain conditions existing in 1947. The States further agreed that those conditions were described and defined in a particular engineering report. But that report turned out to contain material errors. Notwithstanding Texas's objection that the parties had assented to its use, we set aside the flawed study and adopted a new technical document that more accurately depicted the real-world conditions of the compact's specified baseline year. See 446 U.S. 540, 100 S.Ct. 2911, 64 L.Ed.2d 485 (1980)(per curiam) (setting aside the old document); 462 U.S., at 562-563, 103 S.Ct. 2558(describing the litigation); 467 U.S. 1238, 104 S.Ct. 3505, 82 L.Ed.2d 816 (1984)(approving the new document); 482 U.S., at 127, 107 S.Ct. 2279(describing that approval).
Similarly, in Kansas v. Colorado,543 U.S. 86, 125 S.Ct. 526, 160 L.Ed.2d 418 (2004), we modified an agreement to ensure that it would correctly measure Colorado's compliance with the Arkansas River Compact. The parties had consented to use a computer model on a year-by-year basis to gauge their consumption of water.
*1062See id.,at 102, 125 S.Ct. 526("[B]oth [States] agreed to the use of annual measurement"). But after a time, a special master determined that annual accounting produced serious errors, whereas employing a 10-year measuring period accurately determined compact compliance. Over Kansas's protest, we accordingly approved the Master's alteration of the parties' agreement to assess compliance each year. And in countering Kansas's objection to the introduction of a 10-year measuring period, we posited that the compact's drafters, albeit unaware of "complex computer modeling[,] ... would have preferred accurate measurement." Ibid.10
The teaching of those cases applies as well to this one: In each, this Court's authority to devise "fair and equitable solutions" to interstate water disputes encompasses modifying a technical agreement to correct material errors in the way it operates and thus align it with the compacting States' intended apportionment. Texas v. New Mexico,482 U.S., at 134, 107 S.Ct. 2279; cf. Kansas v. Colorado,543 U.S., at 102, 125 S.Ct. 526("After all, a 'credit' for surplus water that rests upon inaccurate measurement is not really a credit at all"). Much as in Texas v. New Mexicoand Kansas v. Colorado,the subsidiary Accounting Procedures here failed to accurately measure what they were supposed to. Modifying those Procedures does no more than make them consonant with the Compact and Settlement, ensuring that they help to realize, rather than frustrate, the agreed-upon division of water.
Indeed, the case for modification is still stronger here, because (as we explain below) the Accounting Procedures as written affirmatively violate the Compact. That accord is the supreme law in this case: As the States explicitly recognized, they could not change the Compact's terms even if they tried. See Settlement § I(D) ("[T]his Stipulation and the Proposed Consent Judgment are not intended to, nor could they, change the States' respective rights and obligations under the Compact"). That is a function of the Compact's status as federal law, which binds the States unless and until Congress says otherwise. And Congress, of course, has not said otherwise here. To enter into a settlement contrary to the Compact is to violate a federal statute. See Vermont v. New York,417 U.S. 270, 278, 94 S.Ct. 2248, 41 L.Ed.2d 61 (1974)(per curiam). And as we have discussed, our equitable authority to grant remedies is at its apex when public rights and obligations are thus *1063implicated. See Porter,328 U.S., at 398, 66 S.Ct. 1086; supra,at 1052 - 1053.
The Accounting Procedures' treatment of imported water first conflicts with the Compact by going beyond its boundaries-in essence, by regulating water ultra vires. According to its terms, the Compact pertains, and pertains only, to "virgin water supply originating in" the Republican River Basin. Compact Art. III; see supra,at 1049, 1059 - 1060. The agreement's very first Article drives that point home: "The physical and other conditions peculiar to the Basin constitute the basis for this compact," and nothing in it relates to any other waterway. To divide or otherwise regulate streams outsidethe Basin, the States would have to enter into a separate agreement and gain congressional approval. (The reason no one thought the Settlement needed such consent is precisely because it purported to stay within the Compact's limits. See Settlement § I(D)) And yet, the Accounting Procedures have the effect of including such outside water within the Compact's apportionment scheme (by counting its use against a State's allotment). The Procedures make water from the Platte subject to the Compact, in contravention of its scope; or conversely stated, they expand the Compact's prescribed scope to cover water from the Platte. That is not within the States' authority.
What is more, the Procedures' treatment of imported water deprives Nebraska of its rights under the Compact to the Basin's own water supply. That is because the inescapable effect of charging Nebraska for the use of imported water, as the Procedures do, is to reduce the amount of Republican River water the State may consume. Suppose the Compact grants 100 units of Republican River water to Nebraska and Kansas alike; and further assume that the Accounting Procedures count 10 units of Platte River water toward Nebraska's allotment. That means Nebraska may now consume only 90 units of Republican River water (or else pay Kansas damages). The Procedures thus change the States' shares of Basin water, to Nebraska's detriment: Nebraska now has less, and Kansas relatively more, than the Compact allows. That, too, lies outside what the States can do.
In light of all the above, we think the Master's proposed solution the best one possible. The 5-run formula that he recommends conforms the Procedures to both the Compact and the Settlement by excluding imported water from the calculation of each State's consumption. See Report 55-56; ibr.US_Case_Law.Schema.Case_Body:v1">id., at App. F. Kansas has not provided any workable alternative to align the Accounting Procedures with the Compact and Settlement. Nor has Kansas credibly shown that this simple change will introduce any other inaccuracy into Compact accounting. See id.,at 58-68. The amendment will damage Kansas in no way other than by taking away something to which it is not entitled. In another case, with another history, we might prefer to instruct the parties to figure out for themselves how to bring the Accounting Procedures into line with the Compact. See New York v. New Jersey,256 U.S. 296, 313, 41 S.Ct. 492, 65 L.Ed. 937 (1921)(noting that negotiation is usually the best way to solve interstate disputes). But we doubt that further discussion about this issue will prove productive. Arbitration has already failed to produce agreement about how to correct the Procedures. See supra,at 1050 - 1051. And before the Special Master, both parties indicated that further "dispute resolution proceedings before the RRCA or an arbitrator" would be "futile." Report 69 (quoting Case Management Order No. 9 ¶ 5 (Jan. 25, 2013)). We accordingly adopt the Master's recommendation to amend the Accounting Procedures *1064so that they no longer charge Nebraska for imported water.
V
Nebraska argues here for a cramped view of our authority to order disgorgement. Kansas argues for a similarly restrictive idea of our power to modify a technical document. We think each has too narrow an understanding of this Court's role in disputes arising from compacts apportioning interstate streams. The Court has broad remedial authority in such cases to enforce the compact's terms. Here, compelling Nebraska to disgorge profits deters it from taking advantage of its upstream position to appropriate more water than the Compact allows. And amending the Accounting Procedures ensures that the Compact's provisions will govern the division of the Republican River Basin's (and only that Basin's) water supply. Both remedies safeguard the Compact; both insist that States live within its law. Accordingly, we adopt all of the Special Master's recommendations.
It is so ordered.